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K–12 Standards

Calculus

Other Arkansas Mathematics Standards sets

Limits & ContinuityLC

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    Identify and Calculate Limits: Students determine the limit of a function at a value numerically, graphically, and analytically. 

    1. 1

      Identify vertical asymptotes in rational and logarithmic functions by identifying locations where the function value approaches infinity; estimate limits numerically and graphically; calculate limits analytically:C.LC.1

      1. 1

        Algebraic simplificationC.LC.1.1

      2. 2

        Direct substitutionC.LC.1.2

      3. 3

        One-sided limitsC.LC.1.3

      4. 4

        RationalizationC.LC.1.4

    2. 2

      Calculate infinite limits and use the result to identify vertical asymptotes in rational and logarithmic functions. C.LC.2

    3. 3

      Calculate limits at infinity and use the result to identify horizontal asymptotes in rational and exponential functions.C.LC.3

    4. 4

      Calculate limits at infinity and use the result to identify unbounded behavior in rational, exponential, and logarithmic functions.C.LC.4

    5. 5

      Identify and classify graphically, algebraically, and numerically if a discontinuity is removable or nonremovable; identify the three conditions that must exist in order for a function to be continuous at 𝑥 = 𝑎: C.LC.5

      1. 1

        𝑓(𝑎) is definedC.LC.5.1

      2. 2

        The limit as 𝑥 approaches 𝑎 of 𝑓(𝑥) equals 𝑓(𝑎)C.LC.5.2

      3. 3

        The limit as 𝑥 approaches 𝑎 of 𝑓(𝑥) existsC.LC.5.3

    6. 6

      Apply the Intermediate Value Theorem for continuous functions.C.LC.6

DerivativesD

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    Equation of a Tangent Line: Students use derivatives to solve problems both theoretically and in real-world context.  

    1. 1

      Approximate the derivative:C.D.1

      1. 1

        Graphically by finding the slope of a tangent line drawn to a curve at a given point. C.D.1.1

      2. 2

        Numerically by using the difference quotient. C.D.1.2

    2. 2

      Find the equation of the tangent line using the definition of derivative.C.D.2

    3. 3

      Establish and apply that differentiability implies continuity, but continuity does not necessarily imply differentiability.C.D.3

    4. 4

      Compare the characteristic of graphs of 𝑓 and 𝑓’: C.D.4

      1. 1

        Generate the graph of 𝑓 given the graph of 𝑓’ and vice versa.C.D.4.1

      2. 2

        Establish the relationship between the increasing and decreasing behavior of 𝑓 and the sign of 𝑓’.C.D.4.2

      3. 3

        Identify maxima and minima as points where increasing and decreasing behavior change. C.D.4.3

    5. 5

      Apply the Mean Value Theorem on a given interval.C.D.5

    6. 6.

      Compare the characteristic of graphs of 𝑓, 𝑓’, and 𝑓”: C.D.6

      1. 1

        Generate the graphs of 𝑓 and 𝑓′ given the graph of 𝑓” and vice versa.C.D.6.1

      2. 2

        Establish the relationship between the concavity of 𝑓 and the sign of 𝑓”.C.D.6.2

      3. 3

        Identify points of inflection as points where concavity changes.C.D.6.3

    7. 7

      Find derivatives of functions using: C.D.7

      1. 1

        Power ruleC.D.7.1

      2. 2

        Product ruleC.D.7.2

      3. 3

        Quotient ruleC.D.7.3

    8. 8

      Find derivatives of:C.D.8

      1. 1

        An implicitly defined equationC.D.8.1

      2. 2

        Composite functions using chain ruleC.D.8.2

      3. 3

        Exponential and logarithmic functions C.D.8.3

      4. 4

        Functions requiring the use of more than one differentiation ruleC.D.8.4

    9. 9

      Find the equation of:C.D.9

      1. 1

        A line tangent to the graph of a function at a point C.D.9.1

      2. 2

        A normal line to the graph of a function at a point C.D.9.2

    10. 10

      Solve application problems involving:C.D.10

      1. 1

        OptimizationC.D.10.1

      2. 2

        Related ratesC.D.10.2

    11. 11

      Interpret the derivative as a rate of change and varied applied contexts. C.D.11

      1. 1

        Contexts include: velocity, speed, and accelerationC.D.11.1

IntegralsI

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    Define the Definite Integral: Students apply techniques of integration to solve problems, both theoretically and in contextual models that represent realworld phenomena. 

    1. 1

      Define the definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval.C.I.1

      1. 1

        If 𝑓 is a real, continuous function defined on [𝑎, 𝑏] and 𝐹 is an antiderivative of 𝑓 in [𝑎, 𝑏], then ∫ 𝑓(𝑥)𝑑𝑥 = 𝐹(𝑏) − 𝐹(𝑎) 𝑏 𝑎 .C.I.1.1

    2. 2

      Determine the area between two curves and identify the definite integral as the area of the region bounded by two curves.C.I.2

    3. 3

      Apply the Fundamental Theorem of Calculus to solve contextual models that represent real-world phenomena. C.I.3

    4. 4

      Find the general solution to indefinite integrals. C.I.4

    5. 5

      Determine the antiderivative of a function using rules of basic differentiation, and solve problems using the techniques of antidifferentiation including but not limited to power rule and u-substitution.C.I.5

    6. 6

      Estimate definite integrals by using Riemann sums (left, right, midpoint, and trapezoidal) and identify the definite integral as a limit of Riemann sums.C.I.6

    7. 7

      Explore applications of integration.C.I.7

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Frequently asked questions

What grade levels do these standards cover?
Grade 9, Grade 10, Grade 11, and Grade 12
Where can I read the official document?
ARKANSAS MATHEMATICS STANDARDS

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